The CoSTAR project is constructing case-study methods for accessing teachers’ and students’ understandings of the same lessons. We videotape mathematics instruction in one classroom everyday for several weeks and pursue the teacher’s and a subset of students’ understandings of the recorded lessons through concurrent weekly interviews. Coordinated research on teachers and students in the same classrooms promises deeper insights into the connections between classroom teaching and learning. We conduct the project in a middle-school that is using the Connected Mathematics Project materials. These are reform-oriented materials whose development was funded by the National Science Foundation.